Gröbner Bases of Modules over Reduction Rings Original Research Article

Reduction rings are rings in which the Gröbner bases approach is possible, i.e., the Gröbner basis of an ideal in a reduction ring can be computed using Buchberger′s algorithm. We show that one can also compute Gröbner bases of modules over reduction rings. Our approach is much more general than other approaches to compute Gröbner bases of modules, in the sense that it applies to many more rings, not just polynomial rings over fields.